# Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging

arXiv: https://arxiv.org/abs/2502.06591 · HTML: https://mlsanity.com/paper/2502.06591/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 76 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [Inverse Compositional Spatial Transformer Networks](https://mlsanity.com/paper/1612.03897/) (2016)
- [Differentiable Divergences Between Time Series](https://mlsanity.com/paper/2010.08354/) (2020)
- [Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation](https://mlsanity.com/paper/1510.02795/) (2015)
- [Temporal Transformer Networks: Joint Learning of Invariant and Discriminative Time Warping](https://mlsanity.com/paper/1906.05947/) (2019)
- [Explicit Disentanglement of Appearance and Perspective in Generative Models](https://mlsanity.com/paper/1906.11881/) (2019)
- [Time Series Alignment with Global Invariances](https://mlsanity.com/paper/2002.03848/) (2020)
- [Continuous Piecewise-Affine Based Motion Model for Image Animation](https://mlsanity.com/paper/2401.09146/) (2024)
- [Probabilistic Spatial Transformer Networks](https://mlsanity.com/paper/2004.03637/) (2020)
- [Closed-Form Diffeomorphic Transformations for Time Series Alignment](https://mlsanity.com/paper/2206.08107/) (2022)
- [Neural Time Warping For Multiple Sequence Alignment](https://mlsanity.com/paper/2006.15753/) (2020)
- [A Deep Moving-camera Background Model](https://mlsanity.com/paper/2209.07923/) (2022)
- [Trainable Highly-expressive Activation Functions](https://mlsanity.com/paper/2407.07564/) (2024)
- [SpaceJAM: a Lightweight and Regularization-free Method for Fast Joint Alignment of Images](https://mlsanity.com/paper/2407.11850/) (2024)
- [A Prototypical Triplet Loss for Cover Detection](https://mlsanity.com/paper/1910.09862/) (2019)
- [Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignment](https://mlsanity.com/paper/2106.11911/) (2021)
- [Leveraging Statistical Shape Priors in GAN-based ECG Synthesis](https://mlsanity.com/paper/2211.02626/) (2022)
- [DiGRAF: Diffeomorphic Graph-Adaptive Activation Function](https://mlsanity.com/paper/2407.02013/) (2024)

## Built on by (most cited first, 3 of 3)

- [TimePoint: Accelerated Time Series Alignment via Self-Supervised Keypoint and Descriptor Learning](https://mlsanity.com/paper/2505.23475/) (2025)
- [Deep Time Warping for Multiple Time Series Alignment](https://mlsanity.com/paper/2502.16324/) (2025)
- [Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval](https://mlsanity.com/paper/2609.36809/) (2026)

## Abstract (arXiv)

In time-series analysis, nonlinear temporal misalignment remains a pivotal challenge that forestalls even simple averaging. Since its introduction, the Diffeomorphic Temporal Alignment Net (DTAN), which we first introduced (Weber et al., 2019) and further developed in (Weber & Freifeld, 2023), has proven itself as an effective solution for this problem (these conference papers are earlier partial versions of the current manuscript). DTAN predicts and applies diffeomorphic transformations in an input-dependent manner, thus facilitating the joint alignment (JA) and averaging of time-series ensembles in an unsupervised or a weakly-supervised manner. The inherent challenges of the weakly/unsupervised setting, particularly the risk of trivial solutions through excessive signal distortion, are mitigated using either one of two distinct strategies: 1) a regularization term for warps; 2) using the Inverse Consistency Averaging Error (ICAE). The latter is a novel, regularization-free approach which also facilitates the JA of variable-length signals. We also further extend our framework to incorporate multi-task learning (MT-DTAN), enabling simultaneous time-series alignment and classification. Additionally, we conduct a comprehensive evaluation of different backbone architectures, demonstrating their efficacy in time-series alignment tasks. Finally, we showcase the utility of our approach in enabling Principal Component Analysis (PCA) for misaligned time-series data. Extensive experiments across 128 UCR datasets validate the superiority of our approach over contemporary averaging methods, including both traditional and learning-based approaches, marking a significant advancement in the field of time-series analysis.